You should be able to see that the "interior angle" of the triangle, at the point where the two first sides connect, is 180- 45= 135 degrees. You have a triangle with angle 145 degrees and adjacent sides of lengths 150 and 50. (That is not a "right triangle".)
Use the "cosine law": where a, b, and c are the lengths of the three sides and C is the angle opposite c- i.e. between a and b so that "c" is the length of the actual path of the airplane.
Once you know that length you can use the sine law, , to calculate angle "B", opposite side b, the side that was representing the wind. That is the angle "off east" that the problem is asking for.